FOM: Re: LEM and determinate truth value

hartry field hf18 at
Sat Mar 7 19:59:35 EST 1998

Neil asks what kind of *justification* one might have for using the
classical law of excluded middle (A or not-A) on vague or indeterminate
sentences; and says he thought that the only justification ever offered for
the use of excluded middle was the principle of bivalence (that all
sentences are true or false).  Not so: the supervaluationist view that truth
is *truth in all of a certain nonempty class of interpretations* preserves
classical logic while rejecting bivalence, and it is perhaps the most widely
accepted approach to vague and indeterminate language.  

Myself I prefer a slight variant of supervaluationism (really just a
notational variant, I think): what the supervaluationist says about truth, I
say about determinate truth.  For truth itself, I take "'p' is true" to be
equivalent to "p".  So if George is borderline bald, we have both that
George is either bald or not, and that 'george is bald' is either true or
false; but not that 'George is bald' is either determinately true or
determinately false.  

Similarly, I think that the continuum hypothesis lacks determinate truth
value.  But by either supervaluationism or the variant just proposed, I can
assert that either CH or not CH.  And by the variant of supervaluationism I
can even assert that CH is either true or false.  It's a view that allows
the proponent of the view that CH is indeterminate to say most of what
people who believe CH determinate say.  So we can accept the (overwhelming!)
arguments for the indeterminacy of CH, without any revision of our
mathematical practice.  All that gets revised is our philosophical
commentaries on what we are doing. --Hartry Field  

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